Psychologist Examines Retention of Mathematical Knowledge

Harry P. Bahrick, director of the memory-research program at Ohio
Wesleyan University, has made several long-term studies of the links
between memory and learning.

In a recent paper, entitled "Lifetime Maintenance of High School
Mathematics Content," which he discussed during a recent forum held by
the American Psychological Association at the National Press Club, he
argues that by extending the period of time over which students acquire
mathematical knowledge, the amount of knowledge retained over a
lifetime may be increased dramatically.

To compile the data for the study, Mr. Bahrick administered
multiple-choice questions on algebra and plane geometry to a group of
1,726 individuals, ranging in age from students to senior citizens, to
determine their level of mathematical knowledge. He then compared the
test results with responses to questionnaires and student records to
determine how much information the various groups retained.

He discussed his findings, and their implications for precollegiate
educators, with Staff Writer Peter West.

Q. What led you to study the retention of mathematical
capabilities?

A. I think it's terribly important for educators to find out more
about what will make knowledge last longer.

Presently, we have good reason to be6lieve that even a month or two
after [students] take exams there are very substantial declines in
[their] performance.

So you spend a lot of time, and effort, and money, and you get
results that last a few months.

The entire cost-benefit ratio of education is a function of what
will make the knowledge last. We need to know what these tradeoffs are
so that we can make intelligent decisions about what to teach.

Q. Could you explain the relevance of your findings to precollegiate
education?

A. One very relevant finding is there is a greater retention of
material that is taught [both] in pre-algebra and algebra than the
material that is taught only in pre-algebra. That indicates that with
substantially more rehearsal, or practice, the yield per hour would go
up by a very large factor indeed.

I'm fairly confident that if nothing were done except [scheduling
classes] fewer times a week for more years, the resulting longevity of
knowledge would be far, far longer.

In quasi-experimental work that I have done with languages, I've
found that longer exposure to knowledge yielded a far larger residue
[of knowledge] over a longer period of time.

Q. Are the findings of your research1papplicable across-the-board to
students of all levels of ability?

A. The rate of forgetting over time does not appear to be a factor
of ability. The slope of the retention functions is very much
influenced by the conditions that we can influence, not by ability, or
achievement, or aptitude.

Q. In your presentation you indicated that your research is unusual
because it violates generally held beliefs about valid psychological
techniques. What are the implications of those differences for those
who would apply your research findings?

A. Memory experiments typically are done over minutes, hours, days,
or, occasionally, weeks, and, as a result, the only kinds of material
that you can examine are those you can learn in a laboratory.

But that method excludes study of virtually all [long-term]
learning. The retention intervals have to be years, and you can't
control what the person does over these years. It simply can't be done.
So the choice is not to do it or to do it with non-experimental
methods.

It was difficult to get money for this originally, but I believe
that the prevailing climate is now more permissive.

Q. What are the implications for precollegiate policymakers who wish
to improve the quality of mathematics instruction and the amount of
knowledge retained by their students?

A. I would increase the percentage of the content from higher
[level] courses that is also taught in the lower [level] courses. And I
would search for [knowledge] that can be introduced earlier and
repeated that way.

I would also spread the instruction out over a few years and try to
have the courses meet less frequently during the week.

You also could run [courses such as] geometry and algebra in
parallel. I see no reason why we couldn't start with both in the 9th
grade.

Some subject matter is sequential and does not permit parallel
teaching, but, where it is possible, I would run them in parallel and
run them over two or three years.

If we did that, I'm fairly certain that the quality of the knowledge
would be noticeably improved and the knowledge retained over a longer
period.

Notice: We recently upgraded our comments. (Learn more here.) If you are logged in as a subscriber or registered user and already have a Display Name on edweek.org, you can post comments. If you do not already have a Display Name, please create one here.

Ground Rules for Posting
We encourage lively debate, but please be respectful of others. Profanity and personal attacks are prohibited. By commenting, you are agreeing to abide by our user agreement.
All comments are public.